de Sitter Vacua & pUniverses

TL;DR

This paper extends the $p$-Schwinger model to de Sitter space, showing that discrete global symmetries can be spontaneously broken, resulting in multiple de Sitter invariant vacua, and explores their implications in quantum gravity.

Contribution

It demonstrates that the $p$-Schwinger model's symmetry-breaking features persist in de Sitter space and explores the existence of multiple vacua and their potential microstate interpretation in quantum gravity.

Findings

Discrete symmetries are spontaneously broken in de Sitter space.

Multiple de Sitter invariant vacua exist in the $p$-Schwinger model.

A semiclassical de Sitter saddle appears at large Nf in the coupled gravity theory.

Abstract

We analyze a simple extension of the Schwinger model, which we refer to as the $p$-Schwinger model, on a de Sitter background. In this theory, the charged massless fermions carry non-unit integer charge $p$. In Minkowski space, the $p$-Schwinger model has discrete zero- and one-form global symmetries that are spontaneously broken, yielding $p$ degenerate ground states. We demonstrate that these features persist upon placing the $p$-Schwinger model on a global de Sitter background, establishing that such discrete global symmetries can be spontaneously broken for quantum field theories in de Sitter space. In particular, the theory is endowed with $p$ distinct, but locally-indistinguishable, de Sitter invariant states, the de Sitter vacua, satisfying the Hadamard property. We couple a variant of the $p$-Schwinger model with ${\rm N}_{\rm f}$ flavors to quantum gravity with $\Lambda>0$, and demonstrate the existence of a semiclassical de Sitter saddle at large ${\rm N}_{\rm f}$. In the gravitational theory, the $p$ de Sitter invariant vacua are speculatively interpreted as microstates of the de Sitter horizon in the low-energy effective field theory.